Confidence intervals

The test was developed in the 1980s for screening donated blood for the presence of
HIV. The test is designed to detect antibodies, substances produced in the body of donors car-
rying the virus; however, the test is not 100% accurate. The developer of the test claimed that
the test would produce fewer than 5% false positives and fewer than 1% false negatives. In
order to evaluate the accuracy of the test, 1,000 persons known to have HIV and10,000 per-
sons known to not have HIV were given the test. The following results were tabulated:

True State of Patient
Test Result Has HIV Does Not Have HIV Total
Positive Test 993 591 1,584
Negative Test 7 9,409 9,416
Total 1,000 10,000 11,000

a. Place a 95% confidence interval on the proportion of false positives produced by the test.
b. Is there substantial evidence (alpha=.05 ) that the test produces less than 5% false
positives?

upper question continued:

Place a 95% confidence interval on the proportion of false negatives produced by
thetest.
b. Is there substantial evidence ( ) that the test produces less than 1% false
negatives?
c. Which of the two types of errors, false positives or false negatives, do you think is
more crucial to public safety? Explain your reasoning.
(Ott. An Introduction to Statistical Methods and Data Analysis, 6th Edition. Brooks/Cole/CourseSmart, 12/30/2008. 547).
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